To find the x-intercept and y-intercept of the line given by the equation \(-3x + 9y = 18\), we can proceed as follows:
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Finding the x-intercept: The x-intercept occurs where \(y = 0\). Substituting \(y = 0\) into the equation: \[ -3x + 9(0) = 18 \implies -3x = 18 \implies x = -6 \] Thus, the x-intercept is \((-6, 0)\).
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Finding the y-intercept: The y-intercept occurs where \(x = 0\). Substituting \(x = 0\) into the equation: \[ -3(0) + 9y = 18 \implies 9y = 18 \implies y = 2 \] Thus, the y-intercept is \((0, 2)\).
Based on our calculations, the x-intercept is \(-6\) and the y-intercept is \(2\).
The correct option is: x-intercept is –6; y-intercept is 2.